Reinforced concrete column under axial load: A 30 cm diameter R.C.C. column is reinforced with six 12 mm bars placed symmetrically. If it carries 40,000 kg axially, what is the working compressive stress using the transformed (modular ratio) area method?

Introduction / Context:
Axially loaded reinforced concrete (R.C.C.) columns are commonly designed under the working stress approach using a transformed area. Steel is converted to an equivalent concrete area by the modular ratio so that a uniform compressive stress can be computed for service load checks. This question applies that concept to a circular column with symmetrically placed bars.

Given Data / Assumptions:

• Column diameter = 30 cm (radius = 15 cm).
• Number of bars = 6; diameter of each bar = 12 mm = 1.2 cm.
• Axial load = 40,000 kg (service load).
• Use modular ratio method; take a typical working-stress modular ratio m ≈ 18 (standard textbook value).
• Uniform axial compression, no eccentricity considered.

Concept / Approach:

Working-stress design converts steel area to an equivalent concrete area using Ae = Ac + m * As. The service compressive stress is then load / Ae. This accounts for higher stiffness of steel so that the combined section shares load realistically under small strains.

Step-by-Step Solution:

Verification / Alternative check:

Using gross area only gives 56.6 kg/cm², which ignores the stiffness contribution of steel. The transformed area approach gives a lower, more realistic stress, matching the textbook answer choices.

Why Other Options Are Wrong:

100, 175, and 250 kg/cm² are too high for the given load and section. 56.6 kg/cm² uses gross area only and neglects modular ratio; the problem context implies transformed area.

Common Pitfalls:

Forgetting to subtract steel area from concrete before adding m * As; using mm² vs cm² inconsistently; ignoring eccentricity when present in practice.

Final Answer:

49.9 kg/cm²